We would be much more likely to reach a correct theory of cultural change if the attempt to understand the history of human institutions on the cheap, by making analogies with organic evolution, were abandoned. What we need instead is the much more difficult effort to construct a theory of historical causation that flows directly from the phenomena to be explained.

The preceding paragraph in the document explains how he reached this conclusion. It's a philosophical argument about how best to do science. Lewontin says he doesn't think giving "simple explanations for phenomena that are complex and diverse" is very scientific. That's an odd argument - since building simple models for complex phenomena is a big part of what science is all about. From this evidence, it seems at least possible that Lewontin's failure to appreciate cultural evolution arose from his faulty scientific epistemology.

This is all rather ironic - since his 1970 paper The Units of Selection got the basics of cultural evolution correct.